# Harmonic Mean

Reviewed by Sujaini | Updated on Oct 05, 2020

Catalogue

## What is Harmonic Mean?

The harmonic mean is a type of numerical average determined by dividing the number of observations by the inverse of each number in the sequence. Therefore, the harmonic mean is the inverse of the inverse arithmetical mean.

The harmonic mean helps to locate multiplicative or negative fractional relationships without thinking about common denominators. Harmonic means are often used to calculate ordinary things like rates (for example, the average travel speed given multiple trip duration).

For finance, the weighted harmonic mean is used to combine multiples, such as price-earnings ratio, since it gives equal weight to every data point.

For finance, the weighted harmonic mean is used to combine multiples, such as price-earnings ratio, as it gives equal weight to each data point. Using weighted arithmetic mean to combine such proportions would give more weight to high data points than low data points because the price-earnings ratios are not price-normalised while the earnings are equalised.

## Harmonic Mean vs Arithmetic Mean and Geometric Mean

Many methods of estimating averages include simple arithmetic mean and average geometric mean. The arithmetic average is the sum of a number series, divided by the count of the number series. In case you were asked to find the class average of test scores, you would add up all the students' test scores, and then divide that total by the number of students.

The geometric mean is the average of several items and is typically used to calculate the output effects of an investment or portfolio. It is defined as "the nth root product of n numbers". When dealing with percentages that are derived from values, the geometric mean must be used while the regular arithmetic mean deals with the costs themselves.